exploratory factor analysis ii

Question 1

Scree plot useful for…

Answer 1

Deciding how many factors to keep

Question 2

Two possible criteria for scree plot

Answer 2

Cut off where the eigenvalues fall approx. linearly (‘inflection point’)

If variables had previously been z-standardised, cut off where lambdhax < 1. K1 rule

Question 3

Interpretations of factors based on factor loadings

Answer 3

PCA does not care how easy they are to interpret.
Only cares about
- Orthogonality
- and extraction of maximum variance

To make the interpretation easier, one can further rotate the coordinate system
This is specific to Factor Analysis (no longer PCA)

Question 4

Orthogonal rotation

Answer 4

Rotate factors 90 deg etc.

Question 5

Oblique rotation

Answer 5

Angle does not remain 90deg, changed to fit factors

Fits both boths
Distinct, simple structure
However, angle change

Question 6

Rotation techniques

Answer 6

Factor analysis goes beyond PCA in that it involves further rotation of the principal components with the objective to make the factor loadings more distinct (simple structure)

Question 7

Varimax rotation

Answer 7

• Most commonly used technique:
  · Orthogonal rotation, meaning the factors remain uncorrelated
  · maximises the variance of the factor loadings for each factor (meaning there is large heterogeneity of these…)

Question 8

Oblimin / Promax rotation:

Answer 8

• Frequently used technique:
  · Factors loose their orthogonality - allow correlations to achieve ‘simple structure’
  (factors nevertheless provide non-redundant information, since they rotate Principal components, see map illustration)
  · Promax is simpler and quicker than Oblimin

Question 9

If we have no external validators (e.g. a priori knowledge about the underlying latent variables from different sources)….

Answer 9

neither factor solutions are wrong or right, they are equivalent

Question 10

Bartlett test of sphericity

Answer 10

if significant, the covariance matrix is suitable for analysis.
- If a covariance matrix is spherical, there is no need to run a factor analysis because the raw data variables are already (mostly) orthogonal in the first place

Question 11

2. Kaiser Meyer Olkin test for “sampling adequacy”

Answer 11

• Reports the proportion of variance across variables that is shared (with at least one other variable), relative to the total variance (=shared variance + sum of variance unique to each variable

Question 12

Number of variables over factors, participants (or observations) etc…

Answer 12

· N (participants) / P (items) : between 5:1 and 10:1 recommendable; minimum 100 participants
· P (items) / M (factors) : 4:1
· N (subjects) / M (factors): 6:1

Question 13

• Cross-loadings

Answer 13

· Ideal, if not too many cross-loadings.
· Cross-loadings are factor loadings of variables that have factor loadings of >0.3 on more than one factor, unless the difference to the highest factor is smaller than 0.2 (e.g. loading on F1: 0.7 and on F2: 0.4, then not considered a problem)

Question 14

• Communalities h2

Answer 14

Explains how much variance of one (original, empirically measured) variable is explained by all extracted factors together

Question 15

• Communality & Sample Size

Answer 15

· All communalities (greater )>0.6: N≥100 are sufficient
· Communalities ≈0.5 & only a few factors: 100 < N < 200 sufficient
· Communalities <0.5 & many factors: N>500 needed

Question 16

Eigenvalues

Answer 16

report the proportion of variance explained by each of the new factors